Common Percentage Mistakes and How to Avoid Them

Using the wrong base

Every percentage is a percentage of something. A price that rises from $50 to $60 has gone up 20% (10 ÷ 50), but the same $10 is only about 16.67% of the new price (10 ÷ 60). Before calculating, ask: percent of what?

Adding percentages that have different bases

A 10% rise followed by a 10% fall does not bring you back to where you started. 100 up 10% is 110; 110 down 10% is 99, because the second 10% was taken of a bigger number. For the same reason, two 10% increases make 21%, not 20%.

Mixing up percentage points and percent

If a survey result moves from 40% to 50%, it has risen by 10 percentage points — but by 25 percent, because 10 is a quarter of 40. Both statements are true; they answer different questions. Use “percentage points” for the plain gap between two percentages.

Reversing a percentage the wrong way

If a price after 20% off is $80, the original was not $80 plus 20% ($96). It was $80 ÷ 0.8 = $100. To undo a percentage change, divide by its multiplier instead of applying the opposite percentage.

Rounding too early

Rounding in the middle of a calculation adds up. A third rounded to 33% and then applied to 1,200 gives 396, while the unrounded 33.33…% gives 400. Keep full precision until the final step.

Percentages over 100 and below zero

• An increase can be any size: going from 20 to 70 is a 250% increase.
• A positive quantity can fall by at most 100% unless it goes below zero, so “prices fell 150%” usually signals a mistake.
• Percentage change from zero is undefined — there is no base to divide by.